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Author: Christian Lindorfer
Publisher: Springer
ISBN: 3658247649
Category : Mathematics
Languages : en
Pages : 72
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Book Description
The connective constant of a quasi-transitive infinite graph is a measure for the asymptotic growth rate of the number of self-avoiding walks of length n from a given starting vertex. On edge-labelled graphs the formal language of self-avoiding walks is generated by a formal grammar, which can be used to calculate the connective constant of the graph. Christian Lindorfer discusses the methods in some examples, including the infinite ladder-graph and the sandwich of two regular infinite trees.
Author: Christian Lindorfer
Publisher: Springer
ISBN: 3658247649
Category : Mathematics
Languages : en
Pages : 72
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Book Description
The connective constant of a quasi-transitive infinite graph is a measure for the asymptotic growth rate of the number of self-avoiding walks of length n from a given starting vertex. On edge-labelled graphs the formal language of self-avoiding walks is generated by a formal grammar, which can be used to calculate the connective constant of the graph. Christian Lindorfer discusses the methods in some examples, including the infinite ladder-graph and the sandwich of two regular infinite trees.
Author: Neal Madras
Publisher: Springer Science & Business Media
ISBN: 1461241324
Category : Mathematics
Languages : en
Pages : 433
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Book Description
A self-avoiding walk is a path on a lattice that does not visit the same site more than once. In spite of this simple definition, many of the most basic questions about this model are difficult to resolve in a mathematically rigorous fashion. In particular, we do not know much about how far an n step self-avoiding walk typically travels from its starting point, or even how many such walks there are. These and other important questions about the self-avoiding walk remain unsolved in the rigorous mathematical sense, although the physics and chemistry communities have reached consensus on the answers by a variety of nonrigorous methods, including computer simulations. But there has been progress among mathematicians as well, much of it in the last decade, and the primary goal of this book is to give an account of the current state of the art as far as rigorous results are concerned. A second goal of this book is to discuss some of the applications of the self-avoiding walk in physics and chemistry, and to describe some of the nonrigorous methods used in those fields. The model originated in chem istry several decades ago as a model for long-chain polymer molecules. Since then it has become an important model in statistical physics, as it exhibits critical behaviour analogous to that occurring in the Ising model and related systems such as percolation.
Author: Wim van Saarloos
Publisher: Princeton University Press
ISBN: 0691191301
Category : Science
Languages : en
Pages : 622
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Book Description
"Soft matter science is an interdisciplinary field at the interface of physics, biology, chemistry, engineering, and materials science. It encompasses colloids, polymers, and liquid crystals as well as rapidly emerging topics such as metamaterials, memory formation and learning in matter, bioactive systems, and artificial life. This textbook introduces key phenomena and concepts in soft matter from a modern perspective, marrying established knowledge with the latest developments and applications. The presentation integrates statistical mechanics, dynamical systems, and hydrodynamic approaches, emphasizing conservation laws and broken symmetries as guiding principles while paying attention to computational and machine learning advances. The book features introductory chapters on fluid mechanics, elasticity, and stochastic phenomena and also covers advanced topics such as pattern formation and active matter. it discusses technological applications as well as relevant phenomena in the life sciences and offers perspectives on emerging research directions"--
Author: Jason Scott Bode
Publisher:
ISBN:
Category :
Languages : en
Pages : 116
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Book Description
Author: Oscar H. Ibarra
Publisher: Springer Science & Business Media
ISBN: 3540405615
Category : Computers
Languages : en
Pages : 324
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Book Description
Automata theory is the foundation of computer science. Its applications have spread to almost all areas of computer science and many other disciplines. In addition, there is a growing number of software systems designed to manipulate automata, regular expressions, grammars, and related structures. This volume contains 24 regular papers from the 8th International Conference on Implementation and Application of Automata (CIAA 2003) held in Santa Barbara, CA, USA, in July 2003 covering various topics in the theory, implementation, and application of automata and related structures. It also includes the abstracts of two invited lectures as well as the abstracts of the poster papers displayed during the conference.
Author: M. Lothaire
Publisher: Cambridge University Press
ISBN: 9780521848022
Category : Computers
Languages : en
Pages : 646
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Publisher Description
Author: Library of Congress. Cataloging Policy and Support Office
Publisher:
ISBN:
Category : Subject headings, Library of Congress
Languages : en
Pages : 1924
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Author: Library of Congress
Publisher:
ISBN:
Category : Subject headings, Library of Congress
Languages : en
Pages : 1128
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Book Description
Author: Anton Bovier
Publisher: Springer
ISBN: 3319193392
Category : Science
Languages : en
Pages : 254
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Book Description
Focusing on the mathematics that lies at the intersection of probability theory, statistical physics, combinatorics and computer science, this volume collects together lecture notes on recent developments in the area. The common ground of these subjects is perhaps best described by the three terms in the title: Random Walks, Random Fields and Disordered Systems. The specific topics covered include a study of Branching Brownian Motion from the perspective of disordered (spin-glass) systems, a detailed analysis of weakly self-avoiding random walks in four spatial dimensions via methods of field theory and the renormalization group, a study of phase transitions in disordered discrete structures using a rigorous version of the cavity method, a survey of recent work on interacting polymers in the ballisticity regime and, finally, a treatise on two-dimensional loop-soup models and their connection to conformally invariant systems and the Gaussian Free Field. The notes are aimed at early graduate students with a modest background in probability and mathematical physics, although they could also be enjoyed by seasoned researchers interested in learning about recent advances in the above fields.
Author: Prabodh Shukla
Publisher: Mittal Publications
ISBN:
Category : Amorphous substances
Languages : en
Pages : 210
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Book Description
